The lambda is in the
amplitude.
I assume FEFF does not integrate over the
distribution of distances, which is where the term in question comes from.
That is, FEFF
calculates A (complex) in
chi(k) =
Im(A(k)*exp(-lambda*R+2*i*k*R)/R^2)
for a single R, but what you want with a
non-0 ss (Artemis' notation for sigma2) is
chi(k,ss) =
<Im(A(k)*exp(-lambda*R+2*i*k*R))/R^2>
where <...> is the average over a
Gaussian distribution of R with second moment equal to ss. The derivation,
for
any who are interested, starts with setting
R = R0+dr and approximating 1/R^2 as (1/R0^2)*exp(-2*dr/R0) to
get
chi(k,ss) =
Im[(A(k)/R^2)*Integral{Exp(-[(lambda+2/R0)+2*i*k]*dr-dr^2/(2*ss)),dr}/Integral{Exp(-dr^2/(2*ss),dr}]
(Mathematica notation).
Completing the square and doing the
integral yields the cited term (except
with a 2/R0 not 1/R0) as well as the familiar
exp(-2*ss*k^2) amplitude. Typically,
the term is question is pretty small.
It results in a distance shift of
ss*(1/lambda+2/R0). If ss=0.01A^2 (fairly hefty), R0=2A and lambda =
0.1A^-1, then we get
a shift of 0.01A. With an ss=0.01A^2,
one might expect anharmonic effects of that order. I also did not include
in the above
any R dependence of A(k), either in
magnitude or phase due to curved-wave effects. Bruce, any idea if those
are ever significant
in this context? I suspect
not.
Therefore, the question is whether, if you
tell FEFF that there's a ss, it adds in the above factors, and whether
IFEFFIT/Artemis
do that, assuming you care about a
<~0.01A shift which would probably exist in any reference spectrum as
well.
mam
----- Original Message -----
Sent: Monday, April 04, 2011 2:33
PM
Subject: Re: [Ifeffit] Third cumulant in
DWF
> On Monday, April 04, 2011 05:25:39 pm Ping, Yuan
wrote:
>> Does the math expression in IFEFFIT include the term
-4k*sigma2*(1/labmda
>> +1/R) in the phase? If yes, the 1st cumulant is
sigma1= R+dR. If no,
>> sigma1= R+dR+2*sigma2*(1/labmda +1/R). It this
correct?
>
> When Ifeffit evaluates the exafs equation, it includes
lamdba from the
> Feff calculation.
>
> B
>
> --
>
> Bruce Ravel ------------------------------------
bravel@bnl.gov
>
> National Institute of Standards and
Technology
> Synchrotron Methods Group at NSLS --- Beamlines U7A,
X24A, X23A2
> Building 535A
> Upton NY, 11973
>
> My homepage: http://xafs.org/BruceRavel
> EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/
>
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